Решить систему sin x+sin y=1/2, sin x*sin y=-1/2

sinx + siny = 1/2 sinx * siny = -1/2 sinx = 1/2 - siny (1/2 - siny)*siny = -1/2 sinx = 1/2 - siny 1/2siny - sin²y + 1/2 = 0 siny = t 1/2t - t² + 1/2 = 0 t² - 1/2t - 1/2 = 0 2t² - t - 1 = 0 t = 1 t = -1/2 siny = 1 siny = -1/2 sinx₁ = 1/2 - siny₁ siny₁ = 1 sinx₁ = -1/2 siny₁ = 1 x₁ = -π/6 + 2πn x₂ = -5π/6 + 2πn y₁ = π/2 + 2πn sinx₃ = 1/2 - siny₂ siny₂ = -1/2 sinx₃ = 1 siny₂ = -1/2 x₃ = π/2 + 2πn y₂ = -π/6 + 2πn y₃ = -5π/6 + 2πn Ответ: (π/2 + 2πn; -π/6 + 2πn); (π/2 + 2πn; -5π/6 + 2πn); (-π/6 + 2πn; π/2 + 2πn); (-5π/6 + 2πn; π/2 + 2πn); n∈Z